%I #4 Oct 20 2013 11:06:28
%S 23,25,32,52,122,133,137,155,157,173,175,203,205,212,221,223,227,229,
%T 230,232,236,238,245,247,250,254,256,263,265,272,274,278,283,287,292,
%U 302,313,317,320,322,326,328,331,335,337,353,355,359,362,371,373,377
%N Numbers n with property that sum of digits is prime and number of prime digits is prime.
%H Harvey P. Dale, <a href="/A093805/b093805.txt">Table of n, a(n) for n = 1..1000</a>
%e a(1)=23, sum of digits 5 is prime, number of prime digits {2,3} 2 is prime,
%e a(5)=122, sum of digits 5 is prime, number of prime digits {2,2} 2 is prime,
%e a(10)=173, sum of digits 11 is prime, number of prime digits {3,7} is prime, ...
%p # Return list of digits stev_sez:=proc(n) local i, tren, st, ans,anstren; ans:=[ ]: anstren:=[ ]: tren:=n: for i while (tren>0) do st:=round( 10*frac(tren/10) ): ans:=[ op(ans), st ]: tren:=trunc(tren/10): end do; for i from nops(ans) to 1 by -1 do anstren:=[ op(anstren), op(i,ans) ]; od; RETURN(anstren); end: # Return number of prime digits ts_stpf:=proc(n) local i, stpf, ans, ans1; ans:=stev_sez(n): ans1:=[ ]: stpf:=0: for i from 1 to nops(ans) do if (isprime(op(i,ans))='true') then stpf:=stpf+1; # stevilo prastevilskih stevk ans1:=[ op(ans1), op(i,ans) ]: # prastevilske stevke fi od; RETURN(stpf) end: # Return sum of digits ts_vsota_stevk:=proc(n) local i, stpf, ans, ans1; ans:=stev_sez(n): ans1:=[ ]: stpf:=0: for i from 1 to nops(ans) do stpf:=stpf+op(i,ans); od; RETURN(stpf) end: ts_pras_vsota_pra_stevk:=proc(n) local i, ans; ans:=[ ]: for i from 1 to n do if ( isprime(ts_vsota_stevk(i)) = 'true' and isprime(ts_stpf(i))='true') then ans:=[ op(ans), i ]: fi od; RETURN(ans) end: ts_pras_vsota_pra_stevk(2000);
%t sdpQ[n_]:=Module[{idn=IntegerDigits[n]},And@@PrimeQ[{Total[idn], Count[ idn,_?PrimeQ]}]]; Select[Range[400],sdpQ] (* _Harvey P. Dale_, Oct 20 2013 *)
%K nonn,base
%O 1,1
%A _Jani Melik_, May 19 2004